Petri Nets Representing the Evolution of Elementary Cellular Automata

Author

Barraga?Œ??n, I. ; Tuoh, J.C.S. ; Medina, J.

Author_Institution

Univ. Autonoma del Estado de Hidalgo, Hidalgo, Mexico

Volume

13

Issue

9

fYear

2015

Firstpage

3103

Lastpage

3112

Abstract

A Petri net (PN) is a directed graph which consists of two kinds of nodes called places and transitions. Besides their graphical representation, PN possess a mathematical formalism based on the incidence matrix and the state equation. In this paper we show that PN can be used as a general tool to represent the evolution of any elementary cellular automaton (ECA). This is performed by matrix operations obtained from the state equation of the PN which represent the cellular automaton and the use of a logical operator. It is presented an algorithm to construct a PN for any ECA and we give some comparative examples between the evolution of markings of the PN and the evolution of the respective ECA.

Keywords

Petri nets; cellular automata; matrix algebra; ECA; PN; Petri nets; directed graph; elementary cellular automata evolution; incidence matrix; logical operator; place; state equation; transition; Adaptation models; Automata; Biological system modeling; Mathematical model; Matrices; Petri nets; Silicon compounds; Petri nets; elementary cellular automata; matrix operations;

fLanguage

English

Journal_Title

Latin America Transactions, IEEE (Revista IEEE America Latina)

Publisher

ieee

ISSN

1548-0992

Type

jour

DOI

10.1109/TLA.2015.7350065

Filename

7350065